XSPECT, estimation of the angular power spectrum by computing cross-power spectra with analytical error bars

Abstract We apply the Tapered Gridded Estimator (TGE) for estimating the cosmological 21-cm power spectrum from 150 MHz GMRT observations which corresponds to the neutral hydrogen (HI) at redshift z = 8.28. Here TGE is used to measure the Multi-frequency Angular Power Spectrum (MAPS) Cℓ(Δν) first, from which we estimate the 21-cm power spectrum P(k⊥, k∥). The data here are much too small for a detection, and the aim is to demonstrate the capabilities of the estimator. We find that the estimated power spectrum is consistent with the expected foreground and noise behaviour. This demonstrates that this estimator correctly estimates the noise bias and subtracts this out to yield an unbiased estimate of the power spectrum. More than $47\%$ of the frequency channels had to be discarded from the data owing to radio-frequency interference, however the estimated power spectrum does not show any artifacts due to missing channels. Finally, we show that it is possible to suppress the foreground contribution by tapering the sky response at large angular separations from the phase center. We combine the k modes within a rectangular region in the ‘EoR window’ to obtain the spherically binned averaged dimensionless power spectra Δ2(k) along with the statistical error σ associated with the measured Δ2(k). The lowest k-bin yields Δ2(k) = (61.47)2 K2 at k = 1.59 Mpc−1, with σ = (27.40)2 K2. We obtain a 2 σ upper limit of (72.66)2 K2 on the mean squared HI 21-cm brightness temperature fluctuations at k = 1.59 Mpc−1.

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THE DEGENERACY PROBLEM IN LAMBDA-CDM COSMOLOGICAL MODELS

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194511001334 ◽

2011 ◽

Vol 03 ◽

pp. 246-253

Author(s):

ARMANDO BERNUI

Keyword(s):

Power Spectrum ◽

Background Radiation ◽

Cosmological Parameters ◽

Power Spectra ◽

Cosmological Models ◽

Microwave Background ◽

Angular Power Spectrum ◽

Statistical Property ◽

Microwave Background Radiation ◽

Degeneracy Problem

Recent measurements of the cosmic microwave background radiation (CMB) from the WMAP satellite led to formulate a successful concordance cosmological model, termed ΛCDM. This model satisfactorily explains the origin and structure of the CMB temperature fluctuations, from small to large angular scales, and moreover it accurately fits –with only six parameters– the CMB angular power spectrum. Despite of their triumphs in describing the observed WMAP data, we notice that some ΛCDM cosmological parameters can attain, due to their error bars, slightly different values and this degree of freedom could produce a significant impact in our understanding of the primordial universe. We are talking about the degeneracy problem, that is cosmological models with parameters that are a little bit different from those given by the ΛCDM model but fits equally well the angular power spectrum of the CMB data. Our interest here is to investigate the Gaussian statistical property, at large angular scales, in two sets of Monte Carlo CMB maps produced by seeding them with slightly different ΛCDM angular power spectra.

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Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

10.20944/preprints201910.0101.v1 ◽

2019 ◽

Author(s):

Herbert W. Hamber ◽

Lu Heng Sunny Yu

Keyword(s):

Power Spectrum ◽

Power Spectra ◽

Angular Spectrum ◽

Scalar Fields ◽

Data Sets ◽

Angular Power Spectrum ◽

Fundamental Parameters ◽

Matter Power Spectrum ◽

The Galaxy ◽

Cosmological Data

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum $ P(k) $ and the CMB temperature angular power spectrum $ C_l $’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of inflation models based on scalar fields. In this work, we review the basic concepts and provide further in-depth investigations. We first update the analysis with more recent data sets and error analysis, and then extend our predictions to the CMB angular spectrum coefficients $ C_l $, which we did not consider previously. Then we investigate further the potential freedoms and uncertainties associated with the fundamental parameters that are part of this picture, and show how recent cosmological data provides significant constraints on these quantities. Overall, we find good general consistency between theory and data, even potentially favoring the gravitationally-motivated picture at the largest scales. We summarize our results by outlining how this picture can be tested in the near future with increasingly accurate astrophysical measurements.

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Intensity and anisotropies of the stochastic gravitational wave background from merging compact binaries in galaxies

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2021/11/032 ◽

2021 ◽

Vol 2021 (11) ◽

pp. 032

Author(s):

Giulia Capurri ◽

Andrea Lapi ◽

Carlo Baccigalupi ◽

Lumen Boco ◽

Giulio Scelfo ◽

...

Keyword(s):

Energy Density ◽

Power Spectrum ◽

Gravitational Wave ◽

Power Spectra ◽

Redshift Distribution ◽

Full Generality ◽

Isotropic Energy ◽

Angular Power Spectrum ◽

Compact Binaries ◽

Gravitational Wave Background

Abstract We investigate the isotropic and anisotropic components of the Stochastic Gravitational Wave Background (SGWB) originated from unresolved merging compact binaries in galaxies. We base our analysis on an empirical approach to galactic astrophysics that allows to follow the evolution of individual systems. We then characterize the energy density of the SGWB as a tracer of the total matter density, in order to compute the angular power spectrum of anisotropies with the Cosmic Linear Anisotropy Solving System (CLASS) public code in full generality. We obtain predictions for the isotropic energy density and for the angular power spectrum of the SGWB anisotropies, and study the prospect for their observations with advanced Laser Interferometer Gravitational-Wave and Virgo Observatories and with the Einstein Telescope. We identify the contributions coming from different type of sources (binary black holes, binary neutron stars and black hole-neutron star) and from different redshifts. We examine in detail the spectral shape of the energy density for all types of sources, comparing the results for the two detectors. We find that the power spectrum of the SGWB anisotropies behaves like a power law on large angular scales and drops at small scales: we explain this behavior in terms of the redshift distribution of sources that contribute most to the signal, and of the sensitivities of the two detectors. Finally, we simulate a high resolution full sky map of the SGWB starting from the power spectra obtained with CLASS and including Poisson statistics and clustering properties.

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Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Universe ◽

10.3390/universe5110216 ◽

2019 ◽

Vol 5 (11) ◽

pp. 216 ◽

Cited By ~ 1

Author(s):

Herbert W. Hamber ◽

Lu Heng Sunny Yu

Keyword(s):

Power Spectrum ◽

Power Spectra ◽

Angular Spectrum ◽

Scalar Fields ◽

Data Sets ◽

Angular Power Spectrum ◽

Fundamental Parameters ◽

Matter Power Spectrum ◽

The Galaxy ◽

Cosmological Data

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum P ( k ) and the CMB temperature angular power spectrum C l ’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of inflation models based on scalar fields. In this work, we review the basic concepts and provide further in-depth investigations. We first update the analysis with more recent data sets and error analysis, and then extend our predictions to the CMB angular spectrum coefficients C l , which we did not consider previously. Then we investigate further the potential freedoms and uncertainties associated with the fundamental parameters that are part of this picture, and show how recent cosmological data provides significant constraints on these quantities. Overall, we find good general consistency between theory and data, even potentially favoring the gravitationally-motivated picture at the largest scales. We summarize our results by outlining how this picture can be tested in the near future with increasingly accurate astrophysical measurements.

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Log-log scale roughness spectroscopy of surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146965 ◽

1993 ◽

Vol 51 ◽

pp. 224-225

Author(s):

P. Fraundorf ◽

B. Armbruster

Keyword(s):

Power Spectrum ◽

Autocorrelation Function ◽

Power Spectra ◽

Scanning Force Microscopy ◽

Scanning Tunneling ◽

Tunneling Microscopy ◽

Force Microscopy ◽

Scanning Force ◽

Lateral Structure ◽

Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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An Accurate Reconstruction of CMB E Mode Signal over Large Angular Scales using Prior Information of CMB Covariance Matrix in ILC Algorithm

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3935 ◽

2020 ◽

Author(s):

Ujjal Purkayastha ◽

Vipin Sudevan ◽

Rajib Saha

Keyword(s):

Power Spectrum ◽

Linear Combination ◽

Covariance Matrix ◽

Large Scale ◽

Prior Information ◽

Future Generation ◽

Temperature Anisotropy ◽

Satellite Mission ◽

Angular Power Spectrum ◽

Accurate Reconstruction

Abstract Recently, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large scale CMB E mode polarization signal, which could probe the ionization history, using simulated observations of 15 frequency CMB polarization maps of future generation Cosmic Origin Explorer (COrE) satellite mission. We find that the clean power spectra, from the usual ILC, are strongly biased due to non zero CMB-foregrounds chance correlations. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E mode reconstruction by incorporating prior information of theoretical E mode angular power spectrum while estimating the weights for linear combination of input maps (Sudevan & Saha 2018b). Using the E mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E mode map and its angular power spectrum. We compare the performance of the usual ILC and the new method over large angular scales and show that the later produces significantly statistically improved results than the former. The new E mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutlipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error.

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The anisotropy of the power spectrum in periodic cosmological simulations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab874 ◽

2021 ◽

Vol 503 (4) ◽

pp. 5638-5645

Author(s):

Gábor Rácz ◽

István Szapudi ◽

István Csabai ◽

László Dobos

Keyword(s):

Dark Matter ◽

Power Spectrum ◽

Large Scale ◽

Cold Dark Matter ◽

Initial Conditions ◽

Power Spectra ◽

Cosmological Simulations ◽

Spherical Collapse ◽

Lower Amplitude ◽

Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

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Statistical modelling of the cosmological dispersion measure

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab170 ◽

2021 ◽

Vol 502 (2) ◽

pp. 2615-2629

Author(s):

Ryuichi Takahashi ◽

Kunihito Ioka ◽

Asuka Mori ◽

Koki Funahashi

Keyword(s):

Dark Matter ◽

Correlation Function ◽

Probability Distribution ◽

Power Spectrum ◽

Free Electron ◽

Statistical Modelling ◽

Dispersion Measure ◽

Host Galaxies ◽

Angular Power Spectrum ◽

Bias Factor

ABSTRACT We have investigated the basic statistics of the cosmological dispersion measure (DM)—such as its mean, variance, probability distribution, angular power spectrum, and correlation function—using the state-of-the-art hydrodynamic simulations, IllustrisTNG300, for the fast radio burst cosmology. To model the DM statistics, we first measured the free-electron abundance and the power spectrum of its spatial fluctuations. The free-electron power spectrum turns out to be consistent with the dark matter power spectrum at large scales, but it is strongly damped at small scales (≲ Mpc) owing to the stellar and active galactic nucleus feedback. The free-electron power spectrum is well modelled using a scale-dependent bias factor (the ratio of its fluctuation amplitude to that of the dark matter). We provide analytical fitting functions for the free-electron abundance and its bias factor. We next constructed mock sky maps of the DM by performing standard ray-tracing simulations with the TNG300 data. The DM statistics are calculated analytically from the fitting functions of the free-electron distribution, which agree well with the simulation results measured from the mock maps. We have also obtained the probability distribution of source redshift for a given DM, which helps in identifying the host galaxies of FRBs from the measured DMs. The angular two-point correlation function of the DM is described by a simple power law, $\xi (\theta) \approx 2400 (\theta /{\rm deg})^{-1} \, {\rm pc}^2 \, {\rm cm}^{-6}$, which we anticipate will be confirmed by future observations when thousands of FRBs are available.

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Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab522 ◽

2021 ◽

Author(s):

Robin E Upham ◽

Michael L Brown ◽

Lee Whittaker

Keyword(s):

Power Spectrum ◽

Random Noise ◽

Power Spectra ◽

Stage Iv ◽

Wishart Distribution ◽

Weak Lensing ◽

Dependence Structure ◽

Gaussian Fields ◽

Non Gaussian ◽

Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

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